diff --git a/draftlogs/5985_change.md b/draftlogs/5985_change.md
new file mode 100644
index 00000000000..90f4977e620
--- /dev/null
+++ b/draftlogs/5985_change.md
@@ -0,0 +1 @@
+- Improve drawing the contour lines in non-linear space e.g. on log axes [[#5985](https://github.com/plotly/plotly.js/pull/5985)], with thanks to @andrew-matteson for the contribution!
diff --git a/src/traces/contour/find_all_paths.js b/src/traces/contour/find_all_paths.js
index 468c8407b63..dd7ba5e1efa 100644
--- a/src/traces/contour/find_all_paths.js
+++ b/src/traces/contour/find_all_paths.js
@@ -269,16 +269,25 @@ function getInterpPx(pi, loc, step) {
     var xa = pi.xaxis;
     var ya = pi.yaxis;
 
+    // Interpolate in linear space, then convert to pixel
     if(step[1]) {
         var dx = (pi.level - zxy) / (pi.z[locy][locx + 1] - zxy);
+        // Interpolate, but protect against NaN linear values for log axis (dx will equal 1 or 0)
+        var dxl =
+            (dx !== 1 ? (1 - dx) * xa.c2l(pi.x[locx]) : 0) +
+            (dx !== 0 ? dx * xa.c2l(pi.x[locx + 1]) : 0);
 
-        return [xa.c2p((1 - dx) * pi.x[locx] + dx * pi.x[locx + 1], true),
+        return [xa.c2p(xa.l2c(dxl), true),
             ya.c2p(pi.y[locy], true),
             locx + dx, locy];
     } else {
         var dy = (pi.level - zxy) / (pi.z[locy + 1][locx] - zxy);
+        var dyl =
+            (dy !== 1 ? (1 - dy) * ya.c2l(pi.y[locy]) : 0) +
+            (dy !== 0 ? dy * ya.c2l(pi.y[locy + 1]) : 0);
+
         return [xa.c2p(pi.x[locx], true),
-            ya.c2p((1 - dy) * pi.y[locy] + dy * pi.y[locy + 1], true),
+            ya.c2p(ya.l2c(dyl), true),
             locx, locy + dy];
     }
 }
diff --git a/test/image/baselines/contour_log.png b/test/image/baselines/contour_log.png
index 8508a6bd7a5..6f3dea9aaa9 100644
Binary files a/test/image/baselines/contour_log.png and b/test/image/baselines/contour_log.png differ
diff --git a/test/image/baselines/contour_nonlinear_interpolation.png b/test/image/baselines/contour_nonlinear_interpolation.png
new file mode 100644
index 00000000000..482696505db
Binary files /dev/null and b/test/image/baselines/contour_nonlinear_interpolation.png differ
diff --git a/test/image/mocks/contour_nonlinear_interpolation.json b/test/image/mocks/contour_nonlinear_interpolation.json
new file mode 100644
index 00000000000..16cc5204d12
--- /dev/null
+++ b/test/image/mocks/contour_nonlinear_interpolation.json
@@ -0,0 +1,72 @@
+{
+  "data": [
+    {
+      "x": [1,2,3,4,5],
+      "y": [1,2,3,4,5],
+      "z": [
+        [0 ,   3.1250,   12.5000,   28.1250,   50.0000],
+        [3.1250,    6.2500,   15.6250,   31.2500,   53.1250],
+        [12.5000,   15.6250,   25.0000,   40.6250,   62.5000],
+        [28.1250,   31.2500,   40.6250,   56.2500,   78.1250],
+        [50.0000,   53.1250,   62.5000,   78.1250,  100.0000]
+      ],
+      "contours": {"start": 10, "end": 90, "size": 10},
+      "type": "contour"
+    },
+    {
+      "x": [1,10,100,1000,10000],
+      "y": [1,2,3,4,5],
+      "z": [
+        [0 ,   3.1250,   12.5000,   28.1250,   50.0000],
+        [3.1250,    6.2500,   15.6250,   31.2500,   53.1250],
+        [12.5000,   15.6250,   25.0000,   40.6250,   62.5000],
+        [28.1250,   31.2500,   40.6250,   56.2500,   78.1250],
+        [50.0000,   53.1250,   62.5000,   78.1250,  100.0000]
+      ],
+      "contours": {"start": 10, "end": 90, "size": 10},
+      "type": "contour",
+      "showscale": false,
+      "xaxis": "x2"
+    },
+    {
+      "x": [1,2,3,4,5],
+      "y": [1,10,100,1000,10000],
+      "z": [
+        [0 ,   3.1250,   12.5000,   28.1250,   50.0000],
+        [3.1250,    6.2500,   15.6250,   31.2500,   53.1250],
+        [12.5000,   15.6250,   25.0000,   40.6250,   62.5000],
+        [28.1250,   31.2500,   40.6250,   56.2500,   78.1250],
+        [50.0000,   53.1250,   62.5000,   78.1250,  100.0000]
+      ],
+      "contours": {"start": 10, "end": 90, "size": 10},
+      "type": "contour",
+      "showscale": false,
+      "yaxis": "y2"
+    },
+    {
+      "x": [1,10,100,1000,10000],
+      "y": [1,10,100,1000,10000],
+      "z": [
+        [0 ,   3.1250,   12.5000,   28.1250,   50.0000],
+        [3.1250,    6.2500,   15.6250,   31.2500,   53.1250],
+        [12.5000,   15.6250,   25.0000,   40.6250,   62.5000],
+        [28.1250,   31.2500,   40.6250,   56.2500,   78.1250],
+        [50.0000,   53.1250,   62.5000,   78.1250,  100.0000]
+      ],
+      "contours": {"start": 10, "end": 90, "size": 10},
+      "type": "contour",
+      "showscale": false,
+      "xaxis": "x2",
+      "yaxis": "y2"
+    }
+  ],
+  "layout": {
+    "xaxis": {"domain": [0, 0.45]},
+    "xaxis2": {"domain": [0.55, 1], "type": "log"},
+    "yaxis": {"domain": [0, 0.45]},
+    "yaxis2": {"domain": [0.55, 1], "type": "log"},
+    "margin": {"l": 50, "b": 50, "r": 110, "t": 10},
+    "width": 500,
+    "height": 400
+  }
+}